Contact open books with flexible pages

TL;DR

This paper establishes a topological obstruction for certain high-dimensional manifolds to admit contact open books with flexible Weinstein pages, linking the existence to the torsion in homology groups.

Contribution

It provides an elementary obstruction criterion based on homology torsion for the existence of contact open books with flexible Weinstein pages in high dimensions.

Findings

Non-existence of contact open books when torsion subgroup is non-zero

Symplectomorphisms of flexible Weinstein manifolds act trivially on cohomology

Examples of non-trivial loops of flexible contact structures

Abstract

We give an elementary topological obstruction for a manifold $M$ of dimension $2q{+}1 \geq 7$ to admit a contact open book with flexible Weinstein pages and $c_1(\pi_2(M)) = 0$: if the torsion subgroup of the $q$-th integral homology group is non-zero, then no such contact open book exists. We achieve this by proving that a symplectomorphism of a flexible Weinstein manifold acts trivially on cohomology. We also produce examples of non-trivial loops of flexible contact structures using related ideas.